Estimation of the Critical Seismic Acceleration for Three-Dimensional Rock Slopes

An analytical approach for the estimating of critical seismic acceleration of rock slopes was proposed in this study. Based on the 3D horn failure model, the critical seismic acceleration coefficient of rock slopes was conducted with the modified Hoek–Brown (MHB) failure criterion in the framework of upper-bound theory for the first time. The nonlinear Hoek–Brown failure criterion is incorporated into the three-dimensional rotational failure mechanism, and a generalized tangent technique is introduced and employed to convert the nonlinear Hoek–Brown failure criterion into a linear criterion. The critical seismic acceleration coefficients obtained from this study were validated by the numerical simulation results based on finite element limit analysis. The agreement showed that the proposed method is effective. Finally, design charts were provided for exceptional cases for practical use in rock engineering.

Earthquake Dynamic Failure Mechanism of Dangerous Rock Based on Dynamics and PFC3D

The dynamic failure mechanism of horizontally layered dangerous rock during earthquakes is complex and only few studies have addressed the combination of particle flow code (PFC) meso-level failure mechanism and mechanical analysis. Based on fracture mechanics and material mechanics we establish a calculation method for the interlayer load and stability coefficient of horizontal layered dangerous rock during strong earthquakes. The method was applied for calculating the stability of a horizontally layered dangerous slope along a highway in the Sichuan Province (China) during earthquakes as a case study. Using a 3D particle flow simulation technology, a PFC3D model of horizontal layered dangerous rock was established. Its dynamic stability, failure mode and Hilbert-Huang 3D time-frequency characteristics are analyzed, and the results of the simulation are largely consistent with the time of the dangerous rock failure as estimated by our new calculation method. Our study documents that as the seismic acceleration gradually increases, the stability coefficient of the rock block fluctuates more violently and the stability coefficient gradually decreases. The stability coefficient of the rock block decreases fastest between 5 and 6 s and the reduction in the stability coefficient is between 0.12 and 0.25. Before the seismic acceleration reaches the maximum, the dangerous rock blocks on the two main controlling structures collapse and get destroyed. 25 s after the earthquake, the failure mode of the dangerous rock is collapse-slip-rotation. We show that earthquakes with frequencies of 0–10 and 250 Hz have the strongest destructive effect on the stability of the horizontally layered dangerous rocks.

Research on Earthquake Acceleration Alarm of Nuclear Power Plant

Almost all nuclear power plants in the world are equipped with seismic instrument system, especially the third generation nuclear power plants in China. When the ground motion measured by four time history accelerometers of containment foundation exceeds the preset threshold, the automatic shutdown trigger signal will be generated. However, from the seismic acceleration characteristics, isolated and prominent single high frequency will be generated the acceleration peak, which has no decisive effect on the seismic response, may cause false alarm, which has a certain impact on the smooth operation of nuclear power plant. According to the principle of three elements of ground motion, this paper puts forward a method that first selects the filtering frequency band which accords with the structural characteristics of nuclear power plants, then synthesizes the three axial acceleration time history, and finally selects the appropriate acceleration peak value for threshold alarm. The results show that the seismic acceleration results obtained by this method can well represent the actual magnitude of acceleration, and can solve the problem of false alarm due to the randomness of single seismic wave, and can be used for automatic reactor shutdown trigger signal of seismic acceleration.

FinDerS(+): Real-Time Earthquake Slip Profiles and Magnitudes Estimated from Backprojected Displacement with Consideration of Fault Source Maturity Gradient

The Finite-Fault Rupture Detector (FinDer) algorithm computes rapid line-source rupture models from high-frequency seismic acceleration amplitudes (PGA). In this paper, we propose two extensions to FinDer, called FinDerS and FinDerS+, which have the advantage of taking into account a geological property of the source fault, its structural maturity, as well as its relation to the earthquake slip distribution. These two new algorithms calculate real-time earthquake slip profiles by backprojecting seismic and/or geodetic displacement amplitudes onto the FinDer line-source. This backprojection is based on a general empirical equation established in previous work that relates dynamic peak ground displacement (PGD) at the stations to on-fault coseismic slip. While FinDerS projects PGD onto the current FinDer line-source, FinDerS+ allows the rupture to grow beyond the current model extent to predict future rupture evolution. For an informed interpolation and smoothing of the estimated slip values, FinDerS and FinDerS+ both employ a generic empirical function that has been shown to relate the along-strike gradient of structural maturity of the ruptured fault, the earthquake slip distribution, and the rupture length. Therefore, while FinDer derives magnitudes from a relatively uncertain and general empirical rupture length-magnitude relations, FinDerS and FinDerS+ provide alternate and better informed magnitude estimates using the mean slip of the profiles derived from the integration of fault source maturity. The two new algorithms can incorporate both seismic strong-motion and geodetic displacement data. In order to recover PGD from strong-motion instruments, we double-integrate and high-pass filter (> 0.075 Hz) the seismic acceleration records. Together, the three algorithms exploit the full spectrum of ground-motions, including high frequencies to derive a source fault model (FinDer) and low frequencies to determine the static offsets along this model (FinDerS and FinDerS+). We test the three algorithms for the 2019 MW 7.1 Ridgecrest (California), 2016 MW 7.0 Kumamoto (Japan), and 2008 MW 7.9 Wenchuan (China) earthquakes. Conclusively, low-frequency PGD data and integration of the fault maturity gradient do not speed-up calculations for these events, but provide additional information on slip distribution and final rupture length, as well as alternative estimates of magnitudes that can be useful to check for consistency across the algorithm suite. The FinDer algorithms systematically outperform previously established real-time PGD-based magnitude estimates in terms of speed and accuracy. The resulting slip distributions can be useful for improved ground-motion prediction given the observed relationship between seismic radiation and fault maturity.

Psuedo static stability analysis of rock slope using patton’s shear criterion

A deterministic model for the factor of safety of an idealized rock mass for planar mode of failure is developed adopting Limit Equilibrium Method (LEM) using Patton’s shear strength criterion and considering practically occurring conditions such as the effect of tension crack, water filled up in tension crack, horizontal and vertical seismic acceleration, rock bolt stabilizing force and surcharge. In the Pseudo-static analysis horizontal seismic acceleration is taken outward from the slope and vertical seismic acceleration is considered in both the direction i.e. towards the direction of gravity (downward) and opposite to the direction of gravity (upward). An expression of normal stresses as limiting criterion has been derived in order to compare the field normal stresses along the failure surface. A detailed parametric study has been presented to investigate the influence of vertical seismic coefficient for both the direction on the stability of rock slope using developed expression. For high normal stress along the failure plane, it is observed that the factor of safety decreases with increase in the value of vertical seismic coefficient towards the direction of gravity and increases linearly with increase in the value of vertical seismic coefficient against the direction of gravity and the opposite trend has been found for lower normal stress. The vertical seismic coefficient against the direction of gravity has predominant effect on factor of safety of rock slope as the rate of increase/decrease of factor of safety with vertical seismic coefficient is more against the direction of gravity. Hence in determining the critical factor of safety, effect of vertical seismic coefficient against the direction of gravity should be considered.

Failure Mechanism of Rock Slopes under Different Seismic Excitation

In earthquake-prone areas, special attention should be paid to the study of the seismic stability of rock slope. Particularly, it becomes much more complicated for the rock slopes with weak structural surfaces. In this study, numerical simulation and the shaking table test are carried out to analyze the influence of seismic excitation and structural surface in different directions on dynamic response of rock slope. Huaping slope with bedding structural surfaces and Lijiang slope with discontinuous structural surfaces besides Jinsha River in Yunnan Province are taken as research objects. The results of numerical simulation and the model test both show that discontinuous structure surface has influence on the propagation characteristics of seismic wavefield. For Huaping slope, the seismic wavefield responses repeatedly between the bedding structural surface and slope surface lead to the increase of the amplification effect. The maximum value of seismic acceleration appears on the empty surface where terrain changes. Horizontal motion plays a leading role in slope failure, and the amplification coefficient of horizontal seismic acceleration is about twice that of vertical seismic acceleration. The failure mode is integral sliding along the bedding structural surface. For Lijiang slope, seismic acceleration field affected by complex structural surface is superimposed repeatedly in local area. The maximum value of seismic acceleration appears in the local area near slope surface. And the dynamic response of slope is controlled by vertical and horizontal motion together. Under the seismic excitation with an intense of 0.336 g in X direction and Z direction, the amplification coefficients of seismic acceleration of Lijiang slope are 3.23 and 3.18, respectively. The vertical motion leads to the cracking of the weak structural surface. Then, Lijiang slope shows the toppling failure mode under the action of horizontal motion.

The Expression of Seismic Surrounding Rock Pressure for a Shallow Tunnel Is Derived Using the Pseudostatic Method

Terzaghi developed a generalized expression of the vertical surrounding rock pressures of shallow tunnels by considering the limit equilibrium of soil masses. In this paper, based on the Terzaghi failure mode, the pseudostatic method is used to derive this expression under seismic loading conditions. The surrounding rock in the fractured zone of the tunnel side wall is analyzed as an isolated body using the limit equilibrium method to obtain the explicit calculation expressions of the horizontal surrounding rock pressures of a shallow tunnel under seismic loading. Case analysis indicates that the proposed method is feasible. In addition, the influence of the seismic acceleration coefficient on surrounding rock pressures is further discussed. The results show that the horizontal surrounding rock pressure decreases with the increase of seismic acceleration coefficients. The vertical surrounding rock pressure increases as the horizontal seismic acceleration coefficient increases, and it decreases with the increase of the vertical seismic acceleration coefficient, and the effect of the seismic acceleration coefficient on surrounding rock pressure is significant. The study results can provide reference for the seismic safety evaluation and structural seismic design of shallow tunnels.